On an official visit to the United States this week, British Prime Minister David Cameron focused his conversations with U.S. President Barack Obama on the war in Afghanistan as well as on efforts to address the crisis in Syria and heightened tensions with Iran. The leaders met to “reaffirm one of the greatest alliances the world has ever known,” Obama said Wednesday.

But some observers wonder whether the importance of what is known as the “special relationship” is beginning to fade. ...